Article

# Categorical aspects of compact quantum groups

Applied Categorical Structures (Impact Factor: 0.38). 08/2012; DOI: 10.1007/s10485-013-9333-8

Source: arXiv

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**ABSTRACT:**Quantum families of maps between quantum spaces are defined and studied. We prove that quantum semigroup (and sometimes quantum group) structures arise naturally on such objects out of more fundamental properties. As particular cases we study quantum semigroups of maps preserving a fixed state and quantum commutants of given quantum families of maps.10/2006; -
##### Article: Compact matrix pseudogroups

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**ABSTRACT:**The compact matrix pseudogroup is a non-commutative compact space endowed with a group structure. The precise definition is given and a number of examples is presented. Among them we have compact group of matrices, duals of discrete groups and twisted (deformed)SU(N) groups. The representation theory is developed. It turns out that the tensor product of representations depends essentially on their order. The existence and the uniqueness of the Haar measure is proved and the orthonormality relations for matrix elements of irreducible representations are derived. The form of these relations differs from that in the group case. This is due to the fact that the Haar measure on pseudogroups is not central in general. The corresponding modular properties are discussed. The Haar measures on the twistedSU(2) group and on the finite matrix pseudogroup are found.Communications in Mathematical Physics 01/1987; 111(4):613-665. · 1.97 Impact Factor -
##### Article: Reflective-coreflective equivalence

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**ABSTRACT:**We explore a curious type of equivalence between certain pairs of reflective and coreflective subcategories. We illustrate with examples involving noncommutative duality for C*-dynamical systems and compact quantum groups, as well as examples where the subcategories are actually isomorphic.Theory and Applications of Categories 12/2010; · 0.54 Impact Factor

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